Probabilistic Choice as a Consequence of Nonlinear (Sub) Optimization
Several researchers have convincingly argued that much probabilistic choice could be the result of (attempted) maximization of some utility function that is nonlinear in the choice probabilities. Others researchers have developed descriptive utility theories that are nonlinear in event probabilities. The present work combines these two viewpoints and motivates utility theories that can be nonlinear in either one or both of choice and event probabilities. The presented theories are based on the idea that most choice situations involve multiple incompatible goals which have to somehow be combined in reaching a decision. In particular, I assume that the decision maker is faced with a vector optimization problem which is converted to a scalar optimization problem, the latter being solved to yield a noninferior solution to the original vector optimization problem. I show that in certain special cases this approach yields the same utility representations as certain other recent nonlinear utility theories. Copyright 1997 Academic Press. Copyright 1997 Academic Press
Marley
AAJ
Department of Psychology, McGill University